Albers, Albert

Metz, Daniel

Nowicki, Lukas

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  50. Internationales  Wissenschaftliches Kolloquium   September, 19-23, 2005   Maschinenbau  von Makro bis Nano / Mechanical Engineering  from Macro to Nano   Proceedings    Fakultät für Maschinenbau / Faculty of Mechanical Engineering     Startseite / Index:  http://www.db-thueringen.de/servlets/DocumentServlet?id=15745 Impressum  Herausgeber: Der Rektor der Technischen Universität llmenau  Univ.-Prof. Dr. rer. nat. habil. Peter Scharff  Redaktion: Referat Marketing und Studentische Angelegenheiten  Andrea Schneider   Fakultät für Maschinenbau  Univ.-Prof. Dr.-Ing. habil. Peter Kurtz, Univ.-Prof. Dipl.-Ing. Dr. med. (habil.) Hartmut Witte, Univ.-Prof. Dr.-Ing. habil. Gerhard Linß,  Dr.-Ing. Beate Schlütter, Dipl.-Biol. Danja Voges,  Dipl.-Ing. Jörg Mämpel, Dipl.-Ing. Susanne Töpfer,  Dipl.-Ing. Silke Stauche  Redaktionsschluss: 31. August 2005 (CD-Rom-Ausgabe)  Technische Realisierung:  Institut für Medientechnik an der TU Ilmenau (CD-Rom-Ausgabe) Dipl.-Ing. Christian Weigel Dipl.-Ing. Helge Drumm Dipl.-Ing. Marco Albrecht  Technische Realisierung: Universitätsbibliothek Ilmenau (Online-Ausgabe)   Postfach 10 05 65  98684 Ilmenau  Verlag:   Verlag ISLE, Betriebsstätte des ISLE e.V.  Werner-von-Siemens-Str. 16  98693 llmenau   © Technische Universität llmenau (Thür.) 2005   Diese Publikationen und alle in ihr enthaltenen Beiträge und Abbildungen sind urheberrechtlich geschützt.   ISBN (Druckausgabe): 3-932633-98-9  (978-3-932633-98-0) ISBN (CD-Rom-Ausgabe): 3-932633-99-7 (978-3-932633-99-7)  Startseite / Index: http://www.db-thueringen.de/servlets/DocumentServlet?id=15745 50. Internationales Wissenschaftliches Kolloquium Technische Universität Ilmenau 19.-23. September 2005  A. Albers / D. Metz / L. Nowicki   Effect of the grain anisotropy on the dimensioning of micro components   ABSTRACT  To ensure the reliable dimensioning of micro components the three-dimensional modelling of the microstructure of micro components is presented. The influence of the material anisotropy of the grains on stresses has been analysed.  Introduction  To reduce development times and costs, modern product development processes employ numerical methods. However, sine new effects e.g. caused by material anisotropy occur in the dimensions of micro technology, the question arises how these can be considered within numerical simulations.  Modelling  Generally microstructures are described with voronoi-mosaics [1] based on a random poisson point process [2]. These computed microstructures than can be meshed with finite elements [3] and analysed by means of a finite element analysis after the material modelling and the application of boundary conditions. This approach is adequate for two-dimensional secnarios [4], but not for three-dimensional examinations due to the complex meshing process of the grains as well as the micro component. In order to modell a three-dimensional microstructure of a micro component, the micro component is meshed as a whole in a first step and the geometrical element centroids are derived. In a second step the micro component  is imported into a software tool and filled with a point field by a random poisson point process. In a next step the finite elements are associated with a point of the field by means of an evaluation of their centroids’ distance to the nearest point. Each finite element is then clearly associated with one random point. Therefore all finite elements of a random point describe one grain. This procedure leads to a meshed micro component with its microstructure. The grains are considered as single crystals with anisotropic behaviour and a random orientation of the crystallographic axes. The orientation is described by Euler angels which are used as random variables. For the analysis material property files with random material orientations based on single crystal values for an arbitrary amount of grains were generated. Results  The influence of the grain anisotropy in the case of complex geometries has been studied at the tooth root of a micro planetary wheel tooth of 17-4PH. The tooth width was 156 µm and the grains size has been varied between 80 µm to 20 µm, which means 30 to 1.000 grains in the whole model. Each model has been analysed with 50 different anisotropic material files.    0.70.80.91.01.11.21.330            70         150         450        1000grainsσani/ σani, M Fig. 1: tensile stress distribution at the tooth root (30 grains on the left, 150 grains in the middle and 1.000 grains on the right) and scatter of the maximum von Mises stresses of the different models. The stress maxima always occur at the tooth root but are varying by means of their amplitude and location within the critical area depending on the anisotropic material file (see figure 1). It can be observed that the scatter decreases with an increasing number of grains in the tooth root. For a given grain size it is therefore possible to derive safety factors for the dimensioning.  Conclusion  A method for the modelling of the microstructure of three-dimensional micro components has been presented. For a reliable dimensioning of micro components with only few grains in critical areas it is now possible to obtain information about the scatter of the stresses which allows an improvement of the dimensioning of those micro components.   Literatur- bzw. Quellenhinweise: [1] D. Stoyan, W. S. Kendall, J. Mecke, Stochastic geometry and its applications (2nd Edition), John Wiley and Sons, Chichester (1995) [2] D. Stoyan, H. Stoyan, Fraktale Formen Punktfelder, Akademie-Verlag (1992) [3] A. Fröhlich, S. Weyer, D. Metz, O. Müller, A. Brückner-Foit, A. Albers, Investigations on the Reliability of FEA Calculations on the Microscopoc Scale, Technical Proceedings of the 2001 International Conference on Computational Nanoscience, Hilton Head Island, South Carolina, USA, 2001, 161-164. [4] Albers A.; Metz D.: Investigations on the Limitations of the FE-Analysis of Micro-Devices, Proceedings of the 4th International Conference, european society for precision engineering and nanotechnology, p. 121-124, 19.05.-20.05.2003, Aachen.   Autorenangaben: Prof. Dr.-Ing. Dr. h.c. Albert Albers Dipl.-Ing. Daniel Metz Dipl.-Ing. Lukas Nowicki Institute of Product Development, University of Karlsruhe, Kaiserstraße 10, 76128 Karlsruhe E-mail: Nowicki@ipek.uni-karlsruhe.de 

Effect of the grain anisotropy on the dimensioning of micro components

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Effect of the grain anisotropy on the dimensioning of micro components

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